I am back with an updated draft after some terrible news around about NASA dismissing these researches. They should not as, otherwise, it could happen as with Galilei having his detractors even not trying to look in the telescope, just dismissing on faith.

I have analysed the case of the frustum and the results appear to be striking. One must admit that geometry comes to rescue not just general relativity. For this particular geometry the cavity can be made susceptible to gravitational effects if your choice of the two radii of the cavity is smart enough. This is something to be confirmed yet, just my theoretical result, but shocking anyway.

It's Eq. 18 that still bothers me a bit. Invoking the Heaviside step function is OK, but I don't see the addl. components being detectable outside the cavity w/o a non-linear term. Maybe I'm missing something ?

That's interesting. The effect of the modified geometry is to couple the resonant mode of the cavity with the external source that in this case is a laser beam. This enters into the correction factor L(v) (sorry for the unfortunate choice of the notation, this is not the same L I use below). I do a first order computation to uncover such a coupling.

OK, I think I see it. Everything is symmetrical to that point. You need the geometry of the frustum to get a residual modulation. (I'm getting there in 10min interludes !)

I have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxes

and see whether we can derive a force for the EM Drive based on Onsager's relations

Still looking for my copy as well ! (old cavity work was on transport properties)

The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmed

I have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxes

and see whether we can derive a force for the EM Drive based on Onsager's relations

Still looking for my copy as well ! (old cavity work was on transport properties)

The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmed

I have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxes

and see whether we can derive a force for the EM Drive based on Onsager's relations

Still looking for my copy as well ! (old cavity work was on transport properties)

The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmed

Yup !

Do you remember if DeGroot mentioned photons ?

That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.

I have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxes

and see whether we can derive a force for the EM Drive based on Onsager's relations

Still looking for my copy as well ! (old cavity work was on transport properties)

The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmed

Yup !

Do you remember if DeGroot mentioned photons ?

That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.

As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect.

Yes. And the way to silence sceptics is to make measurements on a fully-boxed rig - including battery. All these trailing feeds generate pseudo-forces. That would be OK if thrust were Newton level - but it ain't, so it ain't.

The Dynamic Tests of the EM Drive showed a slowly rotating table top of machinery. So sufficient force was being produced to move the equipment 2 metres in a few minutes.

Or a sufficient shift in the centre of mass, for a non perfectly vertical axis.

It is interesting that one of the things that Landsberg shows in 1979 is that the following is not longer true in a gravitational field:

"Thermal equilibrium is equivalent to having a system at uniform temperature throughout"

Right. I have a copy of Kantor, but I find his presentation hard going. He has an introduction ~ p.19.

F. W. Kantor "Information Mechanics", Wiley, 1977

(Heh! Just found Sokolnikoff, noticed all the markup in in chap.4...was working on "Hamiltonian" radar then .... I need to read chap. 3 ! Opps maybe I did ...."Surfaces in space is marked up! Hard gettin' old....)

Nice little treasure trove, good work! Quick reading of some of it seems to be what I've been looking for in one clump. Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!

...(Heh! Just found Sokolnikoff, noticed all the markup in in chap.4...was working on "Hamiltonian" radar then .... I need to read chap. 3 ! Opps maybe I did ...."Surfaces in space is marked up! Hard gettin' old....)

Ivan Sokolnikoff? Which book ? His Higher Math book, his Tensor Analysis book or his less known book with Rainich on the mathematics of relativity ?

...Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!

Not sure about that...wonder how much individual thought process, creativity and imagination is overwhelmed by the huge amount of information available from the Internet nowadays. Many scientists think that it may have the opposite effect on individual intelligence and thought process as the mind needs as much or more exercise (to produce connections of neurons, etc.) as human muscles. With so many "answers" freely available at a click of one's fingers, there is much less exercise of one's brain

Hopefully not a future of people thinking that Physics and Engineering is just a question of getting answers from a huge Internet cookbook of recipes and from black-box computer software instead of using mathematics and experiments to find out how Nature operates...

...(Heh! Just found Sokolnikoff, noticed all the markup in in chap.4...was working on "Hamiltonian" radar then .... I need to read chap. 3 ! Opps maybe I did ...."Surfaces in space is marked up! Hard gettin' old....)

Ivan Sokolnikoff? Which book ? His Higher Math book, his Tensor Analysis book or his less known book with Rainich on the mathematics of relativity ?

Tensor Analysis, '64 edition

I also like the classic (unabridged) Tensor Analysis book by Schouten ("Ricci-Calculus" the one over 500 pages long)

...(Heh! Just found Sokolnikoff, noticed all the markup in in chap.4...was working on "Hamiltonian" radar then .... I need to read chap. 3 ! Opps maybe I did ...."Surfaces in space is marked up! Hard gettin' old....)

Ivan Sokolnikoff? Which book ? His Higher Math book, his Tensor Analysis book or his less known book with Rainich on the mathematics of relativity ?

Tensor Analysis, '64 edition

I also like the classic (unabridged) Tensor Analysis book by Schouten ("Ricci-Calculus" the one over 500 pages long)

...Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!

Not sure about that...wonder how much individual thought process, creativity and imagination is overwhelmed by the huge amount of information available from the Internet nowadays. Many scientists think that it may have the opposite effect on individual intelligence and thought process as the mind needs as much or more exercise (to produce connections of neurons, etc.) as human muscles. With so many "answers" freely available at a click of one's fingers, there is much less exercise of one's brain

I almost always find myself agreeing with you Dr. Rodal, but will respectfully and lightheartedly disagree with you on this. I've heard others take the same position. My experience and observation have been quite the opposite. Those who I know who are Internet savvy, are aware of and participate in online forums, are willing to do deep dives into knowledge areas at a whim using the Internet, are some of the most highly informed and highly evolved people that I know.

Some argue that the quality of information freely available is less than stellar. Again, I would disagree with that notion as well. Wikipedia, for example, has been found to be more accurate in recent years than most printed encyclopedias.

Hooorrrrahh for the Internet, which enables open science pertaining to space flight and other topics, the quick dissemination of information, world-wide collaboration, the trembling of despots, and the dawning of a new age of freedom.

...Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!

Not sure about that...wonder how much individual thought process, creativity and imagination is overwhelmed by the huge amount of information available from the Internet nowadays. Many scientists think that it may have the opposite effect on individual intelligence and thought process as the mind needs as much or more exercise (to produce connections of neurons, etc.) as human muscles. With so many "answers" freely available at a click of one's fingers, there is much less exercise of one's brain

I almost always find myself agreeing with you Dr. Rodal, but will respectfully and lightheartedly disagree with you on this. I've heard others take the same position. My experience and observation have been quite the opposite. Those who I know who are Internet savvy, are aware of and participate in online forums, are willing to do deep dives into knowledge areas at a whim using the Internet, are some of the most highly informed and highly evolved people that I know.

Some argue that the quality of information freely available is less than stellar. Again, I would disagree with that notion as well. Wikipedia, for example, has been found to be more accurate in recent years than most printed encyclopedias.

Hooorrrrahh for the Internet, which enables open science pertaining to space flight and other topics, the quick dissemination of information, world-wide collaboration, the trembling of despots, and the dawning of a new age of freedom.

Notice the reference to space flight in my ranting.

I actually agree, there is always negative and positive aspects to everything but the optimistic viewpoint has prevailed throughout history, and hopefully will continue that way

...Gads I love the internet and wished it was there when I was going to school. I'm not ready to throw the slab of idea and thought meat into the shark pool yet but thanks for the links!!! Kudos!

Not sure about that...wonder how much individual thought process, creativity and imagination is overwhelmed by the huge amount of information available from the Internet nowadays. Many scientists think that it may have the opposite effect on individual intelligence and thought process as the mind needs as much or more exercise (to produce connections of neurons, etc.) as human muscles. With so many "answers" freely available at a click of one's fingers, there is much less exercise of one's brain

That's the truth! When I read we might have attention spans less than a goldfish from the information load I had to agree also. I try to back away from it, go sit in the hot tub, wash dishes, pet the cat, anything to keep on trying to shove more information in that I know will just get jumbled. I get older and those periods of intense concentration get less and less, oh, look a squirrel! Now I'm trying to do stuff like I did when in collage and honestly it's not working as well, I call it the Teflon brain syndrome. One thing hasn't changed, flashes of insight, just by watching the stupid squirrel, and where in the heck they come from, I have no idea.

I have to find my old copy of the book by S. R. De Groot, P. Mazur and other such books I have in boxes

and see whether we can derive a force for the EM Drive based on Onsager's relations

Still looking for my copy as well ! (old cavity work was on transport properties)

The system in that paper is not isolated from the environment. For EM Drive this is not true. You have to cope with a closed system and to understand why third law appears to be violated, if the effect is confirmed

Yup !

Do you remember if DeGroot mentioned photons ?

That book is rather old. I just gave a cursory look and found nothing about photons. You should rather consider the case for electromagnetic radiation. What could make the thing resemble that of a non-isolated system is leakage of radiation out of the cavity. I have to guess that one has built it reducing such losses. The idea to look at gravitational effects, started by Minotti's paper, is because in this case there is not a boundary due to the cavity and system appears to be open (space-time is everywhere). So, the third law would be saved by the expulsion of gravitational momentum. The reason why people in the community of scientists did not consider the case is the smallness of the gravity with respect to all other effects and so, one should not expect it to account for such a measurement.

As you can see from my crude dispersion argument, the g value (of the photons) is much larger than one might naively expect.

It is interesting that one of the things that Landsberg shows in 1979 is that the following is not longer true in a gravitational field:

"Thermal equilibrium is equivalent to having a system at uniform temperature throughout"

That is understandable as the system is open with respect to the gravitational field but this effect should be large enough otherwise the system will retain its equilibrium state. Generally this applies rather well to very large body.